คลังความรู้

The document raises a question about P&L attribution for a single stock option. It defines daily P&L as the change between desk market values and proposes explaining that change through underlying-price delta and gamma effects, implied-volatility vega, and…

The document examines whether stock prices should be martingales when profitable companies generate earnings and investors expect positive returns. Its replies distinguish ordinary prices from discounted or relative asset prices: under no-arbitrage…

The document asks how to close an in-the-money American put in a limited-margin IRA when the option has poor liquidity, uncovered options and short stock positions are prohibited, and exercising would forfeit remaining time value. It considers buying a…

The document describes a proposed stress-testing exercise for a zero-coupon yield curve built from daily observations. The curve combines a money-market-based short tenor with longer tenors interpolated from secondary-market Treasury rates. The author…

The response explains why a volatility surface matters when pricing a Bermudan swaption, an option exercisable on specified dates. It first clarifies that a Bermudan contract need not be exercisable from the beginning of its life, then outlines a model-based…

The document asks how to annualize a Sharpe ratio calculated from monthly returns when those returns are serially correlated. It notes that the usual square-root-of-time scaling assumes uncorrelated returns and raises a specific question about estimating the…

This discussion addresses why a consumer price index can look nearly linear over a selected historical period even though a constant positive inflation rate would compound. It distinguishes an index level from the inflation rate: sustained target inflation…

This note shows how to price a path-dependent lookback call in a two-period binomial model. A European payoff depends only on the terminal asset price, so the two paths that reach the same middle terminal node can be combined and their probabilities added. A…

This discussion considers how to interpret a negative volume entry in a daily market-data file when blanks represent unavailable values. The replies agree that traded volume is not ordinarily negative, while zero volume can occur in some circumstances. One…

This note explains how to connect a Black–Scholes call’s volatility sensitivity to the strike derivative used to price a cash-or-nothing digital option. It starts from the call price and its vega, then shows that the apparent mismatch between a term…

The discussion considers whether Markov chain Monte Carlo is useful for Bayesian inference in quantitative finance. It describes potential applications to estimating hidden-process parameters, including stochastic volatility models, and to inference for…

The exchange addresses how to obtain the underlying input needed to analyze an options dataset when spot prices are unavailable. It suggests estimating a forward price from put and call quotes at a common maturity: identify the strike where their prices are…

The document compares annualized return and volatility calculations based on logarithmic returns and simple returns. For monthly log returns, it describes scaling the mean by the number of periods in a year and scaling standard deviation by the square root…

The document considers two equivalent ways to represent a complete market: state-contingent Arrow-Debreu securities and a set of complex securities whose payoff vectors span all possible states. It asks how to express the equilibrium price of each complex…

The document asks how to read Johansen cointegration test output for two stocks and whether cointegration implies a mean-reverting pair. It presents an initial result indicating one rejected rank hypothesis, followed by a detailed trace-test output where…

A special cash dividend or another corporate action can change an option contract’s deliverable. As a result, an adjusted, nonstandard contract may appear beside a newly issued standard contract with the same underlying, strike, expiration, and call or put…

The document discusses how to hedge a caplet dynamically in a theoretical framework, comparing it with delta hedging an equity call. One suggested approach is to use a forward rate agreement with the relevant expiry, such as an at-the-money FRA, and adjust…

The document explains how to simulate two correlated asset paths under geometric Brownian motion. It starts with a covariance matrix encoding each asset's volatility and their correlation, then factors that matrix with a Cholesky decomposition. Multiplying a…

The document considers whether predicting an asset's current price from other assets has practical value when the market already reports that price. The responses identify data alignment and missing observations as possible uses. A model could estimate…

The document asks how to define a spread for pairs trading after estimating a linear relationship between two asset prices. It compares subtracting the fitted intercept and scaling one price by the estimated gradient with omitting the intercept or simply…

The discussion examines why the variance sensitivity of a variance swap may seem inconsistent with the sensitivities of the options used to replicate it. Under assumptions of continuous paths and a continuum of strikes, the question treats the option…

The discussion distinguishes smoothing a price series from forecasting future values. It gives a recursive exponential-smoothing forecast in which the next estimate updates the current forecast in proportion to the latest observation's forecasting error.…

The discussion asks whether Bitcoin has a quantifiable fair value and how mispricing might be recognized. The answers describe its traded price as an outcome of supply and demand once the market is sufficiently liquid, while emphasizing that speculation is…

The document raises a practical calibration problem: fitting an SVI or SABR volatility surface to mid implied volatility produced a satisfactory fit, while separate fits to bid or ask implied volatility performed poorly. It asks how to fit surfaces to…